Dynamic helicity switching by utilizing metasurfaces is challenging because it requires deep modulation of polarization states. To realize such helicity switching, this paper proposes a dynamic metasurface functioning as a switchable quarter-wave plate, the fast axis of which can be dynamically rotated by 90∘. The device is based on the critical transition of an anisotropic metallic checkerboard, which realizes the deep modulation and simultaneous design of the switchable states. After verifying the functionality of the ideally designed device in a simulation, we tune its structural parameters to realize practical experiments in the terahertz frequency range. By evaluating the fabricated sample with vanadium dioxide, the conductivity of which can be controlled by temperature, its dynamic helicity switching function is demonstrated.